Blackwell Approachability and No-Regret Learning are Equivalent
Blackwell Approachability and No-Regret Learning are Equivalent
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布莱克威尔平易近人和无悔学习是等效的
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
Elad Hazan
中科院分区：
文献类型：
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作者：
Jacob D. Abernethy;P. Bartlett;Elad Hazan
我们认为著名的Blackwell可允许定理与Vector Payos的两人游戏。
O-Regret“用于简单的在线学习问题的算法。我们表明，这种关系实际上更牢固，Blackwell的结果在非常强烈的意义上等同于在线线性优化的遗憾最小化的问题。我们表明，任何任何一个这样的问题的算法可以有效地转换为另一种问题的算法。
We consider the celebrated Blackwell Approachability Theorem for two-player games with vector payos. Blackwell himself previously showed that the theorem implies the existence of a
o-regret" algorithm for a simple online learning problem. We show that this relationship is in fact much stronger, that Blackwell’s result is equivalent to, in a very strong sense, the problem of regret minimization for Online Linear Optimization. We show that any algorithm for one such problem can be eciently converted into an algorithm for the other. We provide one novel application of this reduction: the rst ecient algorithm for calibrated forecasting.